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On binary quartics and the Cassels-Tate pairing

Published version
Peer-reviewed

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Type

Article

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Authors

Fisher, Tom 

Abstract

We use the invariant theory of binary quartics to give a new formula for the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve. Unlike earlier methods, our formula does not require us to solve any conics. An important role in our construction is played by a certain K3 surface defined by a (2,2,2)-form.

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Keywords

Research, ANTS XV

Journal Title

RESEARCH IN NUMBER THEORY

Conference Name

Journal ISSN

2522-0160
2363-9555

Volume Title

Publisher

Springer